Dense torus of an affine toric variety
= Dense torus of an affine toric variety
For a strongly convex rational cone $\sigma$, the group generated by $S=\sigma^\vee\cap M$ is $M$. Inverting its finitely many monomial generators gives $k[M]$, so $\operatorname{Spec}k[M]$ is a dense open <algebraic torus> in $\operatorname{Spec}k[S]$. The map $\chi^m\mapsto\chi^m\otimes\chi^m$ extends torus multiplication to the entire variety.
// Target: geometry-and-topology.bigb